What crystals of small analogs are trying to tell us about cellulose structure

The molecular geometries from crystal structures of 23 small molecules such as cellobiose were reviewed and extrapolated to give model cellulose chains. Within a given model, all monosaccharide units and their linkages are identical so the models are regular helices. Despite fairly large ranges for the glycosidic linkage torsion angles Φ and ψ, 29° and 57°, respectively, there is little variation in the n and h parameters of the model helices. They are extended, with h values (the advance per residue along the helix axis) of 5.04–5.27 A. Some models were slightly right-handed, with n values up to 2.12 residues per helix turn. Left-handed models were in the majority, and their n values were as large as −2.91. These results are consistent with known structures of cellulose and its derivatives. An exception comes from a heavily derivatized cellobiose molecule. It yields right-handed helices with n≈ 4.5 and h≈ 3 A. Because one half turn of this helix reverses the direction of the chain in a compact region, the linkage geometry is a model for chain-folding. Other derivatives that are unable to form the O3⋯O5′ hydrogen bond gave left-handed helices. The puckering of the glucose rings was also surveyed. A number of rings in small molecule structures are puckered to a degree that is similar to the puckering determined for methyl cellotrioside, cellotetraose, cellulose Iβ and cellulose II.